> Suppose we now throw uncountably many darts at the interval. By virtue of the fact each one "determines" (by virtue of being hit) some number in particular, that makes each number they hit "particular" in some sense -- and we know no particular number can ever be hit (at least a second time ;-)> > How many numbers are now left over to be hit?

Infinitely many. The uncomputable's version of uncountable is infinitely larger than the computable's version.:)